On the internal dynamics of Mendelian genetics

This paper offers a revisionist account of the development of Mendelian genetics, focusing on the 'problem of the gene', 1900-1930. I examine conflicting claims about the composition, location, and action of genes posed by Bateson, the Morgan group, and Goldschmidt. Their research programs focused on different phenotypes and were based on different assumptions about the nature of genes. The problem of the gene transcended such specific research programs, but their findings had to be taken into account to solve it. The need to resolve conflicting claims drove Mendelian geneticists to exploit the resources and invade the turf of other disciplines in their search for a sound characterization of the gene. The problem of reconciling conflicting views greatly influenced the development of genetics and provided the stimulus for many of the discoveries made by geneticists from 1900 to 1940.     

A diffusion model for the fate of tandem gene duplicates in diploids

Suppose one chromosome in one member of a population somehow acquires a duplicate copy of the gene, fully linked to the original gene's locus. Preservation is the event that eventually every chromosome in the population is a descendant of the one which initially carried the duplicate. For a haploid population in which the absence of all copies of the gene is lethal, the probability of preservation has recently been estimated via a diffusion approximation. That approximation is shown to carry over to the case of diploids and arbitrary strong selection against the absence of the gene. The techniques used lead to some new results. In the large population limit, it is shown that the relative probability that descendants of a small number of individuals carrying multiple copies of the gene fix in the population is proportional to the number of copies carried. The probability of preservation is approximated when chromosomes carrying two copies of the gene are subject to additional, fully non-functionalizing mutations, thereby modelling either an additional cost of replicating a longer genome, or a partial duplication of the gene. In the latter case the preservation probability depends only on the mutation rate to null for the duplicated portion of the gene.     

Overshooting dynamics in a model adaptive radiation

The history of life is punctuated by repeated periods of unusually rapid evolutionary diversification called adaptive radiation. The dynamics of diversity during a radiation reflect an overshooting pattern with an initial phase of exponential-like increase followed by a slower decline. Much attention has been paid to the factors that drive the increase phase, but far less is known about the causes of the decline phase. Decreases in diversity are rarely associated with climatic changes or catastrophic events, suggesting that they may be an intrinsic consequence of diversification. We experimentally identify the factors responsible for losses in diversity during the later stages of the model adaptive radiation of the bacterium Pseudomonas fluorescens. Proximately, diversity declines because of the loss of biofilm-forming niche specialist morphotypes. We show that this loss occurs despite the presence of strong divergent selection late in the radiation and is associated with continued adaptation of resident niche specialists to both the biotic and abiotic environments. These results suggest that losses of diversity in the latter stages of an adaptive radiation may be a general consequence of diversification through competition and lends support to the idea that the conditions favouring the emergence of diversity are different from those that ensure its long-term maintenance.     

Symmetric competition as a general model for single-species adaptive dynamics

Adaptive dynamics is a widely used framework for modeling long-term evolution of continuous phenotypes. It is based on invasion fitness functions, which determine selection gradients and the canonical equation of adaptive dynamics. Even though the derivation of the adaptive dynamics from a given invasion fitness function is general and model-independent, the derivation of the invasion fitness function itself requires specification of an underlying ecological model. Therefore, evolutionary insights gained from adaptive dynamics models are generally model-dependent. Logistic models for symmetric, frequency-dependent competition are widely used in this context. Such models have the property that the selection gradients derived from them are gradients of scalar functions, which reflects a certain gradient property of the corresponding invasion fitness function. We show that any adaptive dynamics model that is based on an invasion fitness functions with this gradient property can be transformed into a generalized symmetric competition model. This provides a precise delineation of the generality of results derived from competition models. Roughly speaking, to understand the adaptive dynamics of the class of models satisfying a certain gradient condition, one only needs a complete understanding of the adaptive dynamics of symmetric, frequency-dependent competition. We show how this result can be applied to number of basic issues in evolutionary theory.     

A molecular dynamics study of an L-type calcium channel model

In this work, we propose a molecular model of the L-type calcium channel pore from the human cardiac alpha1 subunit. Four glutamic acid residues, the EEEE locus, located at highly conserved P loops (also called SS1-SS2 segments) of the alpha1 subunit, molecularly express the calcium channel selectivity. The proposed alpha-helix structure for the SS1 segment, analyzed through molecular dynamics simulations in aqueous-phase, was validated by the plotting of Ramachandran diagrams for the averaged structures and by the analysis of i and i + 4 helical hydrogen bonding between the amino acid residues. The results of the simulation of the calcium channel model with one and two Ca2+ ions at the binding site are in accordance with mutation studies which suggest that the EEEE locus in the L-type calcium channel must form a single high-affinity binding site. These results suggest that the Ca2+ permeation through the channel would be derived from competition between two ions for the only high-affinity binding site. Furthermore, the experimentally observed blocking of the Na+ flux at micromolar Ca2+ concentrations, probably due to the occupancy of the single high-affinity binding site for one Ca2+, was also reproduced by our model.     

A model for the emergence of adaptive subsystems

We investigate the interaction of learning and evolution in a changing environment. A stable learning capability is regarded as an emergent adaptive system evolved by natural selection of genetic variants. We consider the evolution of an asexual population. Each genotype can have ‘fixed’ and ‘flexible’ alleles. The former express themselves as synaptic connections that remain unchanged during ontogeny and the latter as synapses that can be adjusted through a learning algorithm. Evolution is modelled using genetic algorithms and the changing environment is represented by two optimal synaptic patterns that alternate a fixed number of times during the ‘life’ of the individuals. The amplitude of the change is related to the Hamming distance between the two optimal patterns and the rate of change to the frequency with which both exchange roles. This model is an extension of that of Hinton and Nowlan in which the fitness is given by a probabilistic measure of the Hamming distance to the optimum. We find that two types of evolutionary pathways are possible depending upon how difficult (costly) it is to cope with the changes of the environment. In one case the population loses the learning ability, and the individuals inherit fixed synapses that are optimal in only one of the environmental states. In the other case a flexible subsystem emerges that allows the individuals to adapt to the changes of the environment. The model helps us to understand how an adaptive subsystem can emerge as the result of the tradeoff between the exploitation of a congenital structure and the exploration of the adaptive capabilities practised by learning.     

A terminal dynamics model of the heartbeat

 It is widely assumed that heartbeat dynamics are chaotic, although there has been no evidence confirming such an opinion, and some evidence to the contrary. Additionally, the deterministic assumptions of such dynamics cannot be demonstrated. An alternative model is presented based upon the notion of terminal dynamics, which can more faithfully represent key features of the heartbeat: namely, piecewise determinism, and singular points between beats, which allow for adaptability while maintaining stability. Received: 2 February 1996/Accepted in revised form: 20 May 1996     

Molecular dynamics study of the lauryl alcohol-laurate model bilayer

Molecular dynamics (MD) calculation of the fluid phase lauryl alcohol-laurate bilayer has been executed based on Berendsen's surface-constrained model. Structure and dynamics of the bilayer have been investigated by analyzing the trajectories of the chain configurations. Newly defined correlation functions as well as the conventional ones showed that the tilt and bend of the chain play an important role in the bilayer structure, including behavior of the order parameter. Interpenetration of the layers as well as formation of collectively ordered small domains was also found. The calculated lateral diffusion coefficient was in satisfactory agreement with the experimental one. Successive jumps of the head group, rather than the hydrodynamic continuous motion, were observed. Between the jumps, the molecule librated in a local site. Time-dependent autocorrelation functions showed evidence of several different modes of the chain motion, whose time constant ranged from a few tenths of picoseconds to several tens of picoseconds.     

A mathematical model to study the effects of drugs administration on tumor growth dynamics

A mathematical model for describing the cancer growth dynamics in response to anticancer agents administration in xenograft models is discussed. The model consists of a system of ordinary differential equations involving five parameters (three for describing the untreated growth and two for describing the drug action). Tumor growth in untreated animals is modelled by an exponential growth followed by a linear growth. In treated animals, tumor growth rate is decreased by an additional factor proportional to both drug concentration and proliferating cells. The mathematical analysis conducted in this paper highlights several interesting properties of this tumor growth model. It suggests also effective strategies to design in vivo experiments in animals with potential saving of time and resources. For example, the drug concentration threshold for the tumor eradication, the delay between drug administration and tumor regression, and a time index that measures the efficacy of a treatment are derived and discussed. The model has already been employed in several drug discovery projects. Its application on a data set coming from one of these projects is discussed in this paper.     

On Mendelian randomization analysis of case-control study

Mendelian randomization (MR) analysis uses genotypes as instruments to estimate the causal effect of an exposure in the presence of unobserved confounders. The existing MR methods focus on the data generated from prospective cohort studies. We develop a procedure for studying binary outcomes under a case-control design. The proposed procedure is built upon two working models commonly used for MR analyses and adopts a quasi-empirical likelihood framework to address the ascertainment bias from case-control sampling. We derive various approaches for estimating the causal effect and hypothesis testing under the empirical likelihood framework. We conduct extensive simulation studies to evaluate the proposed methods. We find that the proposed empirical likelihood estimate is less biased than the existing estimates. Among all the approaches considered, the Lagrange multiplier (LM) test has the highest power, and the confidence intervals derived from the LM test have the most accurate coverage. We illustrate the use of our method in MR analysis of prostate cancer case-control data with vitamin D level as exposure and three single nucleotide polymorphisms as instruments.     

A quantum mechanical model of adaptive mutation

The principle that mutations occur randomly with respect to the direction of evolutionary change has been challenged by the phenomenon of adaptive mutations. There is currently no entirely satisfactory theory to account for how a cell can selectively mutate certain genes in response to environmental signals. However, spontaneous mutations are initiated by quantum events such as the shift of a single proton (hydrogen atom) from one site to an adjacent one. We consider here the wave function describing the quantum state of the genome as being in a coherent linear superposition of states describing both the shifted and unshifted protons. Quantum coherence will be destroyed by the process of decoherence in which the quantum state of the genome becomes correlated (entangled) with its surroundings. Using a very simple model we estimate the decoherence times for protons within DNA and demonstrate that quantum coherence may be maintained for biological time-scales. Interaction of the coherent genome wave function with environments containing utilisable substrate will induce rapid decoherence and thereby destroy the superposition of mutant and non-mutant states. We show that this accelerated rate of decoherence may significantly increase the rate of production of the mutated state.     

A generalized adaptive dynamics framework can describe the evolutionary Ultimatum Game

Adaptive dynamics describes the evolution of games where the strategies are continuous functions of some parameters. The standard adaptive dynamics framework assumes that the population is homogeneous at any one time. Differential equations point to the direction of the mutant that has maximum payoff against the resident population. The population then moves towards this mutant. The standard adaptive dynamics formulation cannot deal with games in which the payoff is not differentiable. Here we present a generalized framework which can. We assume that the population is not homogeneous but distributed around an average strategy. This approach can describe the long-term dynamics of the Ultimatum Game and also explain the evolution of fairness in a one-parameter Ultimatum Game.     

Telomere length and metabolic syndrome traits: A Mendelian randomisation study

Observational studies have revealed associations between short leucocyte telomere length (LTL), a TL marker in somatic tissues and multiple Metabolic Syndrome (MetS) traits. Animal studies have supported these findings by showing that increased telomere attrition leads to adipose tissue dysfunction and insulin resistance. We investigated the associations between genetically instrumented LTL and MetS traits using Mendelian Randomisation (MR). Fifty‐two independent variants identified at FDR<0.05 from a genome‐wide association study (GWAS) including 78,592 Europeans and collectively accounting for 2.93% of LTL variance were selected as genetic instruments for LTL. Summary‐level data for MetS traits and for the MetS as a binary phenotype were obtained from the largest publicly available GWAS and two‐sample MR analyses were used to estimate the associations of LTL with these traits. The combined effect of the genetic instruments was modelled using inverse variance weighted regression and sensitivity analyses with MR‐Egger, weighted‐median and MR‐PRESSO were performed to test for and correct horizonal pleiotropy. Genetically instrumented longer LTL was associated with higher waist‐to‐hip ratio adjusted for body mass index (β = 0.045 SD, SE = 0.018, p = 0.01), raised systolic (β = 1.529 mmHg, SE = 0.332, p = 4x10⁻⁶) and diastolic (β = 0.633 mmHg, SE = 0.222, p = 0.004) blood pressure, and increased MetS risk (OR = 1.133, 95% CI 1.057–1.215). Consistent results were obtained in sensitivity analyses, which provided no evidence of unbalanced horizontal pleiotropy. Telomere shortening might not be a major driver of cellular senescence and dysfunction in human adipose tissue. Future experimental studies should examine the mechanistic bases for the links between longer LTL and increased upper‐body fat distribution and raised blood pressure.     

From Mendelian to molecular genetics: the Xiphophorus melanoma model

In human tumor biopsies it is almost impossible to pinpoint the particular molecular abnormalities that determine neoplasia. In animal models where tumorigenesis is initiated by clearly defined genetic events, it is possible to study the genes and their functions that make a normal cell become a fully malignant cancer cell. In the fish Xiphophorus, melanoma can be initiated by simple crossings, and the signaling pathways that govern tumor growth and progression can be delineated. This model offers the prospect of obtaining a complete picture of the molecular changes and regulatory networks underlying tumor formation, which should contribute to a better understanding of some general principles of cancer biology, and identify new targets for melanoma research in particular.     

A steered molecular dynamics method with adaptive direction adjustments

In this paper, a new steered molecular dynamics (SMD) method with adjusting pulling direction is proposed to search an optimum trajectory of ligand dissociation. A multiobjective model and a searching technique based on information entropy with multi-population are developed to optimize the pulling direction. The improved method has been used to dissociate the substrate-bound complex structure of cytochrome P450 3A4-metyrapone. A more favorable dissociation pathway can be gained. The results show that the new pathway obtained by the proposed method has less dissociation time, smaller rupture force and lower energy barrier than that by the conventional SMD.     

A construction method to study the role of incidence in the adaptive dynamics of pathogens with direct and environmental transmission

We study the adaptive dynamics of virulence of a pathogen transmitted both via direct contacts between hosts and via free pathogens that survive in the environment. The model is very flexible with a number of trade-off functions linking virulence to other pathogen-related parameters and with two incidence functions that describe the contact rates between hosts and between a host and free pathogens. Instead of making a priori particular assumptions about the shapes of these functions, we introduce a construction method to create specific pairs of incidence functions such that the model becomes an optimization model. Unfolding the optimization model leads to coexistence of pathogen strains and evolutionary branching of virulence. The construction method is applicable to a wide range of eco-evolutionary models.